Fahn, Matthias und Hadjer, Tahmina Sadat:

How Blackwater Takes Uncle Sam for a Ride - and Why

He Likes It

Munich Discussion Paper No. 2014-12

Department of Economics

University of Munich

Volkswirtschaftliche Fakultät

Ludwig-Maximilians-Universität München

Online at https://doi.org/10.5282/ubm/epub.20832

How Blackwater Takes Uncle Sam for a Ride - and Why He

Likes It∗

A Model of Moral Hazard and Limited Commitment

Matthias Fahn†, Tahmina Sadat Hadjer‡

May 11, 2014

Abstract

Private Military and Security Companies (PMSCs) have been gaining increasing me-

dia and scholarly attention particularly due to their indispensable role in the wars in

Afghanistan 2001 and Iraq 2003. Nevertheless, theoretical insights into the agency prob-

lems inherent when hiring PMSCs and how to optimally incentivize them are scarce. We

study the complex relationship between intervening state, host state, and PMSC, taking

into account the diverging interests of all involved parties as well as potential agency prob-

lems. We develop a theoretical model to characterize a state’s optimal choice whether to

perform a task associated with an intervening mission itself, hire a PMSC and optimally

design the contract, or completely abstain from it.

We find that it might be optimal to hire PMSCs even if they are expected to do a worse

job than the intervening state would do itself. This outcome is especially problematic for

the host state, which prefers associated tasks to be done as good and carefully as possible.

Furthermore, the often-heard call for transparency regarding agreements with PMSCs can

lead to a situation where the latter’s performance gets even worse - namely because the

ability to implicit reward PMSCs for a good performance in the past is reduced.

Keywords: International Conflicts, Private Military and Security Companies, Moral

Hazard, Relational Contracts

JEL-Classification: C72, C73, F51, F53

∗We thank Florian Englmaier, Chris Kinsey, Dirk Leuffen, Robert Powell, Gerald Schneider, and participantsat the 2012 ISA conference (San Diego) for helpful comments.

†Corresponding Author. Affiliation: University of Munich, Department of Economics,matthias.fahn@econ.lmu.de, +49 89 2180 5604.

‡Affiliation: University of Konstanz, Department of Politics and Management, tahmina.sadat-hadjer@uni-konstanz.de.

1

“We are simply not going to go to war without contractors.” (Carter, 2011)

1 Introduction

The current international security architecture has been undergoing tremendous changes within

the last decades. The end of the Cold War in 1990 has disclosed a number of internal armed

conflicts in regions of weak or failed statehood which up to that time were hidden under the

covert of the rivalry of the two superpowers USA and USSR (Gleditsch et al., 2002). Since

1990, though, most leading industrial countries have not been willing to intervene in armed

conflicts anymore, unless their direct strategic interests were in danger (Mandel, 2002; Singer,

2003).

These two contrary developments - the increasing number of armed conflicts around the

world as well as the subliminal disinterest of those countries that would be able to intervene

- have triggered a rising demand for private military and security services. Today, private

military and security companies (henceforth PMSCs) offer a wide range of services, including

combat operations, military assistance, intelligence, operational and logistics support, static

security of individuals and property, advice and training of security forces, de-mining and

weapons destruction, humanitarian aid, research and analysis, and even facility and infrastruc-

ture building (Perlo-Freeman and Sköns, 2008:6; Branovic, 2011:26). The clients of PMSCs

are as diverse as the services they offer, ranging from states and international organizations, to

transnational companies, humanitarian nongovernmental organizations, and even rebel groups

(Singer, 2003:183; Holmqvist, 2005:7; Mathieu and Dearden, 2007). Particularly the wars in

Afghanistan 2001 and Iraq 2003 remarkably increased the use of these companies and showed

plainly that present implementation of international security policy is heavily reliant on the

support of the private military and security industry. According to the report “Transforming

Wartime Contracting” of the U.S. Congress’ Commission on Wartime Contracting1, the US

Department of Defense, the US Department of State and the US Agency for International

Development employed more than 260,000 contractor employees in Afghanistan and in Iraq in

2010. This number exceeds the number of US military and civilian personnel in these countries

at that time. Furthermore, from 2002 through 2011 an estimated $206 billion were spent for

these contracts (CWC, 2011).

However, various incidents have manifested that the collaboration between states and

PMSCs presents new challenges which - due to the distinct nature of the tasks involved -

substantially differ from previously made experiences with subcontracting and privatization.

Several occurrences made clear that states that hire PMSCs rely on agents which have their own

dynamics and engage in moral hazard. According to the Project on Government Oversight’s1The Commission on Wartime Contracting was created by the 110th US Congress. The first commissioners

were appointed in July 2008.

2

Federal Contractor Misconduct Database (FCMD), this misconduct ranges from human rights

violations, poor contract performance, government contract fraud, to cost/labor mischarge.

For instance, in 1999 DynCorp International personnel engaged in human trafficking and forced

prostitution in Bosnia Herzegowina. In 2007 personnel of the company Blackwater Worldwide

shot and killed 17 Iraqi civilians. Due to this incidence, they lost their contracts with the US

government in Iraq but secured new deals with the US government in Afghanistan. In the

same year ArmorGroup International personnel, hired to provide security for the US embassy

in Kabul, organized humiliating sex games and were unable to guarantee the security of the

embassy due to internal inefficiencies (FCMD 2012). In addition, the process of how PMSCs

are selected and how contracts with them are negotiated often seems to be very intransparent

and cannot avoid a sense of corruption (Dickinson, 2007, or Stöber, 2007).

All these issues show quite plainly the implicit risks and imponderabilities of contracting

with PMSCs in contingency operations. Despite these malpractices, PMSCs are constantly

hired by states, though. Hence, the questions arise (1) why states, while being aware of the

complicated agency dilemma inherent when hiring PMSCs, still rely on the services of these

companies and (2) how to set the right incentives for and design contracts with these companies

to act to the best advantage of their principals.

However, the scholarly debate concerning PMSCs has largely focused on normative ques-

tions. Besides, parts of the discussion suffer from polarization - by either condemning or

praising the private military and security industry: Advocates of using PMSCs emphasize

the strong demand for privatized military and security provision and the industry’s role in

filling the security gap (Shearer, 1998; Brooks, 2000). Critics, on the other hand, consider

the strong reliance on PMSCs a threat for state authority and the legitimate use of force and

fear the blurring of responsibilities, the weakening of democratic mechanisms and the legal

grey area that surrounds PMSCs’ activities (Cilliers and Mason, 1999; Musah and Fayemi,

2000). Both sides, though, are clear about the irreversibility of PMSCs’ presence in the cur-

rent international security structure. Hence, a third, more pragmatically oriented, strand of

the literature has focused on how to establish effective regulatory, monitoring, accountability,

and prosecution mechanisms in order to minimize the risks associated with the use of PM-

SCs (Chesterman and Lehnardt, 2007; Cockayne et al., 2009; Francioni and Ronzitti, 2011).

However, studies investigating contextual factors that are conducive to the performance of

PMSCs are rare. This is particularly astonishing regarding the increased reliance and use of

PMSCs not only by states (whether strong or weak) but also by trans-national corporations

or non-governmental organizations (Singer, 2001). To a large extent, this is driven by the

difficulty of finding sufficient empirical evidence. Nevertheless, understanding the mechanisms

that drive PMSCs’ behaviour and identifying parameters which states can influence in order

to induce a desired performance of PMSCs helps us to minimize the risks and benefit from

the advantages associated with the use of PMSCs.

3

The goal of this paper is to shed light on one particular scenario of PMSC-client interaction:

The complex relationship between an intervening state, a host state and a PMSC. We take

into account the diverging interests of all involved parties as well as potential agency problems

and develop a theoretical moral hazard model to analyze a states’s optimal choice whether to

perform a task associated with an international mission itself, engage a PMSC and optimally

design the hiring contract, or completely abstain from doing it.

2 Overview

We develop a theoretical moral hazard model to analyze the optimal behavior of a state

(“principal”, “she”) which has the option to delegate a military or security task to an agent

(“he”), in this case a PMSC. The delegation can take place against the background of various

scenarios; for example it might be that the state is dealing with oppositional groups inside its

territory as it was the case with the missions of Executive Outcomes and Sandline International

in Angola and Sierra Leone in the early 1990s; or it might be that the state aims at improving

its military and security structure like it was the case with the support of the Croatian Army

by MPRI during the Yugoslavian wars in the late 1990s; or it might be that the state plans to

or has already intervened in another country like it has happened during the recent wars in

Iraq and Afghanistan, in which the intervening countries hired various PMSCs to fulfil certain

military and security tasks (see Singer, 2003). However, in the light of any potential scenario

the state has three options: It can carry out the task itself, delegate it to a PMSC, or abstain

from performing it at all.

If the task is supposed to be carried out, the state or the PMSC - depending on whether

the task is delegated or not - decides on the resources they plan to spend, for example how

many people to deploy for the task, their quality, the amount of training they receive, and the

intended time period. All aspects that can determine the success of the mission are subsumed

in a one-dimensional variable, denoted effort. Generally, a higher effort level is associated with

higher costs, but also increases the chances for a good outcome.

The core question is: Why and how would the state choose to delegate the task? We

identify three crucial advantages for states when delegating military and security tasks to

PMSCs:

1. Reducing financial costs: States can reduce financial costs such as retirement, medical

and training costs because PMSCs are paid only when needed. Furthermore, in cases

where countries are involved in interventions or operations that are too extensive for their

available force structure, additional costs, such as recruiting of new military and civilian

personnel, accrue. States can circumvent these costs by hiring specialized PMSCs.

2. Enhancing military effectiveness: States can enhance their military effectiveness because

4

PMSCs are often specialized and possess modern military equipment and skills. In

addition, hiring PMSCs enables the armed forces to free own resources and to concentrate

on core functions.

3. Reducing political costs: States can reduce political costs which arise in the course

of a military operation. There, it seems that states are particularly concerned with

reducing political risks which might arise from high fatalities (Schreier and Caparini,

2005). Shaw (2002) argues that one important aspect of wars these days is to keep risks

away from one’s own military. As an example, he refers to recent military interventions

(the Yugoslav War in the 1990s and the Afghanistan War in 2001) where local allies

on the ground took a great share of battle casualties. He argues that states are more

willing to accept indirect and less visible casualties, i.e. such casualties for which their

own, direct responsibility can be dwarfed. Apparently, civilian casualties and deaths of

regular soldiers count more - in terms of political costs - than casualties of PMSCs.

Within the context of our model, we subsume the first two aspects (reducing financial costs

and enhancing military effectiveness) under the assumption that the variable effort costs the

PMSC faces are lower than those of the state. The last aspect (reducing political costs) is

captured by the assumption that negative outcomes are more harmful to the state if the latter

has been active itself.

However, delegating the task is also associated with an agency problem: Contrary to the

state, the PMSC has no intrinsic interest in achieving the outcome preferred by the principal.

Furthermore, it is not possible or too costly to fully monitor the PMSC’s effort. Instead,

the state can only observe whether it was completed successfully or not. Whereas success is

positively affected by the PMSC’s effort, some uncertainty always prevails, and failure can

even occur if the task has been carried out with all possible care.

In addition, giving the PMSC appropriate incentives is restricted by the extent to which

compensation can be based on the realized outcome. Past experience has shown that contracts

between states and PMSCs are left vague, leaving out potential contingencies and related

consequences (Stöber, 2007). Even though it seems desirable to relate PMSCs’ compensation

to a realized performance measure, it appears very difficult to do so because verification and

enforcement is always limited in the context of contingency operations (Dickinson, 2007).

However, rewarding the PMSC based on performance is certainly not impossible because a

state is likely to have more tasks and missions in the future, for which it potentially needs

PMSCs. Hence, performance-based compensation can indirectly and implicitly be part of the

agreement between state and PMSCs, namely as the expectation of being re-hired for future

tasks and forwarded a rent. Indeed, there is evidence that these considerations play a role

because PMSCs are often not chosen based on a competitive bidding process (Berrios, 2006;

Dickinson, 2007; Ortiz, 2010). Therefore, we assume in the model that discretionary payments

5

based on whether the task was completed successfully are possible but bounded. On the one

hand, they cannot be negative, implying limited liability on the PMSCs’ side. Hence, the

only way to punish the PMSC for doing a bad job is not hiring it for future tasks. On the

other hand, these payments cannot be arbitrarily large but are restricted by the value future

collaborations have for the state (this aspect is achieved by an extension of the basic model,

where we explicitly take the possibility of repeated interaction and the resulting consequences

on the enforceability of rewards into account). If this value is too low, the state only has

limited incentives to honor promises and maintain mutual trust.

We derive three main results that help to better understand the complicated relationship

between states and PMSCs.

1. Even if the agent is expected to do a worse job than the principal would do herself,

delegation can be optimal. Lower (induced) effort of the agent is possible although the

latter faces lower variable costs. This is driven by two aspects: Limited liability on

the agent’s side might make it necessary to give him a rent. This rent increases with

implemented effort, and the principal faces a trade-off between inducing more effort and

rent extraction. Furthermore, the fact that negative outcomes are more harmful to the

state if it has been active itself reduces the optimal power of incentives from the state’s

perspective. This outcome is especially problematic for a potential host state, which -

upon entry - will prefer associated tasks to be done as well and carefully as possible.

Thus, from a host state’s perspective, either less PMSCs should be hired, or the involved

states should set higher incentives. This will be difficult to impose, though, since the

government of the intervening country acts in a way to maximize its own utility.

2. Countries not very active in international missions are less likely to hire PMSCs. The

reason is that a lower frequency of future missions - which are used to “compensate”

PMSCs for good outcomes in the past - restricts the states’ ability to give appropriate

incentives. However, commitment can also be increased by a decline in a country’s abil-

ity to perform certain tasks itself (for example by a reduction of investments into its own

troops). The reason is that promises to compensate the PMSC are more credible if the

alternative options - compared to hiring a PMSC - are worse, and one alternative obvi-

ously is to carry out a mission oneself. Hence, reducing the attractiveness of this option

increases the importance of good relationships with PMSCs and hence a government’s

commitment to maintain them.

3. The government’s reputation in keeping promises after a good outcome is crucial in

incentivizing PMSCs. If rents are forwarded to PMSCs as a reward for a good outcome

in the past, this might appear to be missing a service in return, and is frequently criticized

as inefficient or even containing elements of corruption. We argue that attempts to make

6

the hiring process for PMSCs more transparent - like using competitive bidding processes

- can actually have a negative impact on the performance of PMSCs, because it reduces

a government’s commitment.2

The remainder of the paper proceeds as follows: The next section provides a brief overview

of the economic and political science principal-agent literature on which this paper is based

on and discusses the existent theoretical literature on PMSCs, in particular those which apply

principal-agent theory. Section four presents the model setup, while section five analyzes the

players’ optimal actions in a static setting. Section six extends the model by incorporating

the dynamic nature of the relationship between principal and agent. Section seven examines

the impact of the use of PMSCs on a potential host state. Section eight concludes.

3 Related Literature

Our paper contributes to the theoretical literature on the implications of PMSCs’ rise, influ-

ence, and deployment in crisis and war regions. So far this literature on PMSCs has focused on

diverse topics: One branch of this literature deals with PMSCs’ role in the creation, global per-

ception, and maintenance of the concepts of security and risk (Krahmann 2011, Carmola 2010,

Leander 2005). A second branch focuses on the influence of neo-liberal governmentality on

the private security sector and the use of this concept by private security actors (Abrahamsen

and Williams 2010, Leander and van Munster 2007). A third - and to this paper most related

- branch of the literature examines principal-agent interactions between states and PMSCs,

however only informally. Cockayne (2007), for instance, applies the ideas of principal-agent

theory to the regulation of PMSCs and offers insights for potential risks and opportunities

when contracting with private actors for security services, especially against the background

of legitimacy, authority and rule of law. He reasons that security, particularly with regard to

weak states, risks becoming a product of power and cash rather than a legal right. Dickinson

(2007) discusses possible accountability mechanisms and focuses on the question how to de-

sign and improve contracts in such a way that they ensure efficient monitoring, oversight and

enforcement mechanisms. She particularly calls on non-governmental organizations to strive

towards alternative accountability instruments such as international accreditation regimes and

to mobilize political pressure. Stöber (2007) analyzes the delegation of security to private ac-

tors by conducting a case study of the Iraq War of 2003. He uses a principal-agent approach in

order to examine potential contractual hazards and the possibilities of the principal to enforce

the agent’s compliance to the negotiated contract.

However, even though all these studies use a principal-agent approach, none of them ex-2See Calzolari and Spagnolo (2009), who develop a similar argument for public procurement.

7

amines the questions why it is optimal for the principal to delegate the provision of security to

an agent and how to incentivize the agent optimally (for example by using a formal model),

as does this paper. Hence, compared to the preceding literature the present paper goes one

step further and, thus, makes a noteworthy contribution to the knowledge as well as theory

building in this field of research. To use Feaver’s (2003, p.113) words: “The monopoly on

the legitimate use of force is what distinguishes governments from other institutions. Under-

standing how this monopoly is delegated and controlled is therefore central to the enterprise

of political science.”

Furthemore, this paper is based on the principal-agent moral hazard literature building

on Holmström (1979) and Grossman and Hart (1983), which was initially developed to better

understand employment relationships when an employee’s effort is unobservable. Furthermore,

we relate to different extensions of the original approach, which analyze enforcement problems

that restrict payments to optimally base pay on performance. Innes (1990), for example,

assumes that an agent might be protected by limited liability, implying that his compensation

must not fall below a certain level. In this case, it is necessary to give the agent a rent,

making it optimal for the principal to reduce incentives and consequently implemented effort.

While all these models focus on explicit contracts that reward the agent based on verifiable

performance measures, there has been an increased interest in implicit contracts as a way to

mitigate the moral hazard problem if output or effort can be observed but not verified to an

outside party (see, e.g. Bull 1987, MacLeod and Malcomson 1989, or Levin 2003). In this

case, cooperation can only be sustained within a dynamic game. We think this aspect is also

relevant for the relationship between a government and a PMSC, since compensation based

on the outcome of past performance can only be implicit and for example manifest in future

projects.

4 Model Setup - Static Game

Structure

A country, subsequently denoted as “principal” (or “she”), faces the choice to (1) exercise

a military or security task herself, (2) completely abstain from performing it, or (3) hire a

PMSC, subsequently denoted as “agent” (or “he”), to carry out the task. Military and security

task in this context refer to any kind of such services potentially offered by PMSCs. Each

of the three options causes the realization of different outcomes. This model focues on one

specific task; however, the process will be identical among all of them, as long as there are

no interdependencies. We assume that only one agent is available, but discuss the potential

selection process below. In section 6, we further take into account the possibility that the

agent can be hired repeatedly.

8

If the principal conducts the task herself, she faces fixed costs FP ≥ 0. After starting,

she decides about her effort level eP , which can take any value between zero and one, i.e.,

eP ∈ [0, 1] and is directly chosen by the principal. However, effort is costly, and a higher

level is associated with higher costs. Formally, effort costs are cP (eP ), with cP (eP ) = kPe2P

2 ,

kP > 0. Total costs for the principal, if she conducts the task herself and plans to choose

effort eP , thus amount to CP (eP ) = FP + cP (eP ).

The task can either be a success for the principal or not. This manifests in whether the

initial purpose is met, but also in what happened during the period, for example the number

of own soldiers that have died or other incidents that can have an impact on the domestic

public opinion or the principal’s international reputation. Formally, this is captured by the

resulting outcome YP ∈ {LP , H}, with LP ≤ 0 < H. The subscript in LP captures the fact

that a failure can be assessed differently by the principal, depending on whether she herself or

the agent has been active. Conditional on performing the task, the probability of a success,

i.e., of Y = H, is determined by the principal’s effort, with Prob(Y = H | eP ) = eP .

If the agent is hired instead, he also faces fixed starting costs, FA and can choose effort

eA ∈ [0, 1], which is associated with variable effort costs cA(eA) = kAe2A

2 . Thus, total costs -

borne by the hired agent - are CA(eA) = FA+ kAe2A

2 . The outcome YA can either be LA or H,

with LA ≤ 0 < H. The offer made by the principal consists of an ex ante payment w, as well

as some discretionary compensation b, in the following referred to as bonus. In this setting,

though, it does not refer to direct monetary payments but should rather be interpreted as the

possibility of being rehired by the principal in the future. In the static benchmark model we

assume that the principal can credibly commit to any value of b. However, in section 6 we

endogenize the maximum enforceable value of b if the agent can be hired repeatedly. Then,

the term b is equivalent to the maximum future rent the principal can credibly promise to

forward to the agent.

Furthermore, the agent’s effort is not observable to the principal, but output - as well as

the decision to perform the task triggering the fixed starting costs - is. Thus, the bonus can

only depend on the outcome, i.e., we have b(YA). This implies that the principal can directly

choose effort if she decides to enter herself but is not able to do so when the agent is hired,

and then faces a moral hazard problem. In this case, incentives are given by an appropriate

choice of b(YA).

Players’ Preferences

The principal would like to maximize her utility from the accomplishment of a military or

security task, whereas the agent would like to excercise as little effort as possible. In particular,

the players’ preferences are defined as follows: If the principal conducts the task herself, her

9

utility is uPP = YP −CP (e).3 If the agent is hired, the principal’s payoff is uAP = YA−w−b(YA).

If the principal neither conducts the task herself nor hires the agent, her utility equals uP .

We impose no assumption on the size of uP . For some tasks, however, it might seem sensible

to set uP ≥ LP . For example, combat operations with high civilian fatalities might make the

principal worse off ex post compared to having abstained from the beginning. For other tasks,

like the training of the host country’s security forces in the context of a military intervention,

any action is better than abstaining. In this case, we would have uP < LP .

The agent’s preferences are not affected by the outcome Y , but only depend on the pay-

ments he receives from the principal, as well as the costs he has to bear. Thus, we have

uA = w + b(YA) − CA(eA) if the agent is hired. If not, his payoff is uA, where we make the

normalization uA = 0.

Assumptions

Based on the overview in section 2, we establish some assumptions on the parameters that have

a direct impact on the principal’s preferred choice of action, and then describe and analyze

the interaction between state and PMSC as reflected in our model.

First of all, the agent’s variable costs are lower than the principal’s , i.e., we make

Assumption 1: kP ≥ kA.

We subsume under variable costs expenses such as hiring costs, training costs, pension,

health care, and widow obligations.4 It seems sensible that PMSCs can avoid various costs

the state would have to bear. Moreover, past experiences with PMSCs show that they hire

mostly locals or third-country nationals, who are even less costly (CWC, 2011, p.226).

We impose no assumption on the relationship between FA and FP . Of course, similar

arguments as with variable costs could be used to claim that FP ≥ FA. However, it should be

noted that states already possess an infrastructure, for example for the training of employees,

that can be used for another task at small additional costs.

Next, we impose

Assumption 2: LP ≤ LA

This assumption implies that negative outcomes are more harmful if the principal has been

active herself. As we have already discussed in section 2, we argue that the reputational loss3Note that the principal’s preferences are generally described by the preferences of the state’s government.4According to the Commission on Wartime Contracting, the incremental operating cost to deploy a military

member is estimated to be about $10,000 per year (CWC, 2011:225).

10

for the principal - when she does not succeed in a military operation, or when civilians or

soldiers are killed or involved in criminal activities, or simply the fact that the principal is

involved in controversial military operations which are not supported by the public - should

be larger than when PMSCs had been responsible. Hence, when hiring PMSCs, states can

avoid various political costs which they would have to bear otherwise.

The next assumption is purely technical, and serves to avoid corner solutions (i.e., to make

sure that e < 1)

Assumption 3: (H − LA) < kA

Note that Assumption 3 - together with Assumption 1 - also implies (H − LP ) < kP .

We could not find evidence that PMSCs offficially receive contingent compensation based

on some (verfiable) measure of success. However, we believe that the component of a contingent

compensation is not absent at all but implicitly enters the contract between principal and

agent. Countries hiring contractors might also envisage other missions, and a good experience

with one agent can increase the latter’s prospect of being hired again. Therefore, we add the

contingent payment b, which reflects this possibility, into our model. Our benchmark setup

is a short-cut of this potential repeated interaction. However, the principal will not be able

to credibly promise an arbitrarily high payment because future missions are limited. Hence,

commitment to base payments on YA is possible, but this commitment is limited. We analyze

this aspect in detail in section 6. For now, we impose no upper bound on b.

Moreover, payments are supposed to be non-negative. This reflects the implicit assumption

that the agent is rewarded for a good outcome by being hired in future missions. In case of

a bad outcome, however, the punishment that can be imposed on him cannot be more severe

than not being hired for future tasks or receiving a lower rent in future task.

Hence, we impose

Assumption 4: w, b ≥ 0

Consequently , we have a game of moral hozard with limited liability if the agent is hired,

see Innes (1990) for a general characterization. Our model differs in a sense that the prin-

cipal can also be active herself, but that this is associated with different costs and outcome

parameters.

11

5 Results - Static Game

In the following sections, we analyze the optimal actions when the principal decides to perform

the task herself, then derive the optimal contract if the agent is hired, and finally compare

both options.

Optimal Effort Choice of the Principal

If the principal does not hire the agent but has to decide whether to carry out the task herself

or not to do it at all, her optimal behavior is described by

Proposition 1: If the principal decides not to hire the agent, effort conditional on per-

forming the task is e∗P = (H−LP )kP

. However, performing the task herself is optimal for the

principal if and only if

LP +(H − LP )

2

2kP− FP ≥ uP . (1)

Proof : In the present case, the principal can directly set the effort level. Thus, the problem

to be solved equals

maxeP

uP = ePH + (1− eP )LP − CP (eP ), (2)

s.t. uP ≥ uP . The first-order condition characterizes equilibrium effort given performing the

task (note that this condition is also sufficient, provided our assumptions concerning effort

costs):

(H − LP )− kP eP = 0. (3)

Plugging this into the right hand side of (2) gives (1). Q.E.D.

Thus, more effort is chosen if variable costs kP are lower and if the difference between good

and bad outcome, H − LP , is larger. The same is true for the probability of performing the

task at all, which is also affected by fixed costs, as well as the principal’s utility in the bad

outcome. A lower LP indicates that a failure is very detrimental to the principal’s interest.

For example, the political costs a state has to face in case of a bad outcome can outweigh any

potential gains a military victory provides. In this case, it will be better for the principal to

completely abstain from the task. We briefly illustrate this aspect with the US involvement

in the Vietnam War between 1965 and 1975. Against the background of the Cold War, the

US intervened in the war between the communist North Vietnam and anti-communist South

Vietnam in order to halt the communist expansion. Even though the US was never defeated on

the battlefield, the military involvement in the Vietnam War proved to be a political disaster

12

for the US administration. The domestic public opinion turned against the US involvement

and eventually caused the withdrawal of US troops from Vietnam particularly because of the

brutal acts of war and the high civilian and troop causalities which became known to the US

public during the war (Hess, 2009). In retrospective, one could therefore argue that it would

have been better for the US not to intervene in the Vietnam War in the first place.

Optimal Contract if a Specific Agent is Hired

Now, assume that the principal decides to hire the agent. Here, we assume that all bargaining

power is on the principal’s side, who can therefore determine the terms of the contract. This

could be justified by assuming competition on the PMSCs side. However, due to the exogenous

bounds on compensation (which cannot be negative), the agent might still receive a rent.

Before exploring the agent’s actual effort choice and associated incentives, we look at

first-best effort (from the principal’s perspective) given the agent is hired and take it as a

benchmark. This level would be eFBA = (H−LA)

kAand might or might not be higher than e∗P .5

More precisely, eFBA ≥ e∗P if and only if (H−LA)

(H−LP ) ≥ kAkP

. On the one hand, a lower marginal

effort costs kA in relation to kP makes it more likely to have eFBA ≥ e∗P . On the other hand,

the fact that a bad outcome is worse for the principal if she had performed the task herself

(LA ≥ LP ) works into the opposite direction.

If the agent’s effort was verifiable, it would be optimal to induce eFBA . In this case, offering

a bonus b(e) = cA(eFBA ) would provide sufficient incentives, and the fixed wage would be set

to cover the agent’s fixed costs and outside option, i.e. wA = FA + uA = FA. However,

the agent’s effort is not contractible, and the contingent payment b can only be based on the

realized outcome. Hence, it might be optimal to actually induce an effort level lower than

eFBA . The reason is that due to the agent’s limited liability constraint, the agent must receive

a rent absent fixed costs. If FA is sufficiently small, the agent receives a net rent, and the

principal faces a trade-off between effort maximization and rent extraction. This induces her

to implement an effort level that is below the first-best, even if the latter were enforceable.

Deriving these results, note that due to b being restricted to non-negative values, it will

obviously be optimal to set b(LA) = 0. If high output is realized, the agent receives the

payment b(H) ≡ b. Given an arbitrary payment b, the agent chooses an effort level to maximize

his expected utility. This is captured by the incentive compatibility (IC) constraint

e∗A = argmaxuA = w + eAb+ (1− eA) · 0− CA(eA). (IC)

Equilibrium effort is independent of the fixed payment w, which is set at the beginning of

the relationship and thus cannot be used to give incentives. Since the conditions to use the5eFB

A would be the agent’s effort if the principal were able to directly choose it herself. In this case, theprincipal solves max

eA

eAH + (1− eA)LA − CA(eA), where the first order condition gives eFB

A .

13

first order approach are satisfied6, we have equilibrium effort

e∗A =b

kA.

It follows that, conditional on hiring the agent, the principal sets b and w to

maxuP = eA(H − b) + (1− eA)LA − w,

subject to

e∗A =b

kA(IC)

uA = eAb− kAe2A2

− FA + w ≥ 0 (IR)

w, b ≥ 0 (LL)

Proposition 2: Assume the agent is hired. Then, equilibrium effort depends on FA which

determines whether the agent has to get a rent. More precisly, there exist values FA and FA,

with FA < FA, such that

• Effort is at its efficient level, e∗A = eFBA = (H−LA)

kA, if FA ≥ FA. However, in this case

it can only be optimal to hire the agent if doing nothing is worth than a failure, i.e., if

uP < LA

• Effort is at half its efficient level, e∗A = (H−LA)2kA

, if FA < FA

• Effort lies between eFBA and

eFB

A

2 if FA ≤ FA < FA

The proof to Proposition 2 can be found in Appendix A.

For relatively high fixed costs, the principal does not have to give the agent an extra rent

and thus implements first-best effort. However, this case can only be optimal if doing nothing

is worth than a failure, i.e., if uP < LA. This aspect is further explored in Proposition 5 below.

For low fixed costs, the binding limited liability constraint allows the agent to extract some

rent. Then, the principal faces a trade-off between surplus maximization and rent extraction,

making it optimal to only implement half of first-best effort and paying the agent a rent. For

intermediate levels of fixed costs, this tradeoff is also present. Then, however, it is optimal to

only reduce effort and keep the agent at his outside utility. Thus, effort falls with lower fixed

costs, until it reaches half the efficient level, where it becomes optimal to grant the agent a6For example, see Rogerson (1985).

14

rent. Furthermore, the principal’s payoff decreases with FA as long as FA ≥ FA. For FA < FA,

uAP is independent of FA.

Comparison

In the following, we compare the principal’s decision to either perform the task herself with

her decision to hire the agent. Generally, we can make the following statement.

Lemma 2: Performing the task herself rather than hiring the agent becomes relatively bet-

ter for the principal for higher levels of LP , FA and kA, and for lower levels of LA, FB and

kB. The impact of a higher H is ambigous and depends on the size of kA, kP , LA and LP .

The proof to Lemma 2 can be found in Appendix A. Not surprisingly, it becomes less

attractive to hire the agent if the latter ceteris paribus faces higher operating costs, and if a

bad outcome after performing the task itself, LP , is less problematic. The next proposition

- which is also proven in Appendix A - captures the importance of the difference between

LA and LP , i.e., the principal’s payoff after a failure, dependent on whether the agent was

hired or not. In this case, a larger difference always makes it relatively better to hire the agent.

Proposition 3: A larger difference between LA and LP reduces uPP − uAP .

The fact that the domestic public opinion might be rather indifferent towards the death of

PMSCs personnel compared to the death of regular soldiers leads to a problematic outcome:

It not only reduces the implemented effort if the agent is hired, but also makes it more likely

that the agent is actually chosen. In case of international military interventions, this result

connotes a problem for the country in which the intervention takes place (the host state).

Even though the host state mainly cares about how well the job is done - i.e., about the level

of implemented effort - it is possible that the wrong player (from the host state’s perspective),

namely the PMSC instead of the principal’s own forces, carries out the task. We further

explore this issue in section 7.

Now, we present a further proposition that describes another case of when hiring the agent

is always better than performing the task herself, namely when we assume FP ≥ FA and the

agent’s fixed costs are sufficiently high.

Proposition 4: Assume FP ≥ FA and FA ≥ (H−LA)2

2kA. Then, it is always better for the

principal to hire the agent compared to performing the task herself.

Proof : Note that∂(uP

P−uA

P )∂kP

= − (H−LP )2

2k2P

< 0. Since kP ≥ kA, it is thus sufficient to show

15

that uPP − uAP < 0 for kP = kA.

If kP = kA = k, then uPP − uAP = LP −LA +2H(LA−LP )−(L2

A−L2

P )2k +FA −FP = LP −LA −

(LP − LA)H−LA+H−LP

2k + FA − FP .

Since LA ≥ LP , (H − LA) < kA and thus H−LA+H−LP

2k < 1, uPP − uAP is negative for

FP ≥ FA.

Q.E.D.

Two aspects drive this result. First of all, high fixed costs alleviate the necessity to give

the agent a rent, also making it optimal to induce first-best effort if the agent is hired. Since

the principal’s fixed costs are even higher, the need to compensate the agent for his fixed costs

drives the principal to perform the task herself. Furthermore, LA ≥ LP reduces the principal’s

loss if the task fulfillment is not successful.

However, if the conditions of Proposition 4 are satisfied, the task might not be performed

at all. Above, we described that often it seems sensible to assume LA ≤ uP , i.e., that a failure

of the task gives the principal a lower payoff than if it had abstained from performing it from

the beginning. Then, we have

Proposition 5: Assume FP ≥ FA, FA ≥ (H−LA)2

2kAand uP ≥ LA. Then, it is optimal for

the principal to abstain from performing the task.

Proof : From Proposition 2 above we know that for FA ≥ (H−LA)2

2kA, we have uAP = LA −

(

FA − (H−LA)2

2kA

)

. Since the term in brackets is positive, and since we assume uP ≥ LA, the

condition uAP ≥ uP can never be satisfied. Finally, we can use Proposition 3, stating that the

option of the principal performing the task herself is always dominated by the option of hiring

the agent instead.

Q.E.D.

In all other cases, namely if FP < FA or FA <(H−LA)2

2kA, each option can be optimal,

and the agent even might be hired if this is with lower effort levels. For example, assume

that kP = kA = k and FA <(H−LA)2

8kA. Then, hiring the agent is always associated with

substantially less effort than if the principal performs the task itself. However, the latter can

be optimal, namely if uPP −uAP = LP −LA+ (H−LP )2

2k − (H−LA)2

4k −FP < 0. This is always true

for FP sufficiently large. Moreover, even if FP = 0, this condition can be satisfied, depending

on the difference between LP and LA (see Proposition 3).

16

6 Repeated Interaction and Potential Bounds on b

We already discussed that contingent compensation as an official part of agreements between

governments and PMSCs is basically not observed. Instead, it seems that these components

rather enter implicitly, namely via future collaborations where the agent will receive a rent.

In this section, we incorporate the dynamic nature of the relationship between principal and

agent into our model and analyze the consequences when all contingent compensation must

be self-enforcing, i.e., it must be optimal for the principal to actually forward it to the agent.

We extend the model in the following way: The principal repeatedly faces the same choice

as before, where all aspects of the task - costs, identity of agents and payoffs in case of success

or failure - do not vary over time.7 Furthermore, we abstract from all aspects and tasks of a

mission for which the specific agent is not considered, either because others are better suited

or because the principal is performing it herself. Formally, we analyze an infinitely repeated

game in discrete time, where periods are denoted t = 1, 2, ..., and future period are discounted

with the factor δ < 1 (a complete formal characterization can be found in Appendix B). δ not

only reflects time preferences, but also issues like the frequency with which this kind of task

is carried out or the existence of other, competing agents.

In order to stay as close as possible to the static case, we still use bonus payments made at

the end of a period to reward agents - although we argued that agents are rather compensated

within future projects. However, if we replaced the bonus with a fixed wage wh (with wh =bδ+ w), paid to the agent at the beginning of each period following a successful one, the

following analysis would yield identical outcomes.

The crucial aspect in this section is that it has to be optimal for the principal to actually

forward the bonus to the agent after a success. Hence, the principal must fear a punishment

after failing to do so. This punishment takes the form of a complete loss of trust in the

principal by the agent. In other words, the agent only trusts the principal to make future

bonus payments as long as the latter has not broken any given promise in the past. After

reneging, the principal knows that the agent will not exert effort anymore, and it will generally

not be optimal to hire the agent for any future mission. Furthermore, we restrict our focus

on so-called stationary contracts, i.e. the contract offered by the principal is identical in every

period.8

The present analysis is only interesting if the agent is actually hired in equilibrium. A

necessary condition for this is that hiring the agent is optimal given no upper bound on b

exists. Due to stationarity, this is the case whenever hiring the agent is optimal in the static7This assumption is solely made for concreteness. Letting parameters change stochastically would have no

qualitative impact on our results.8Note that under some circumstances, the principal could benefit from offering a non-stationary contract

(see Fong and Li, 2010, for a theoretical analysis of relational contracts with limited liability). However, thesimplifying assumption of stationary contracts is sufficient to make our point.

17

case, as analyzed above. From now on, we will hence impose

Assumption 5: In the static case analyzed above, it is optimal to hire the agent, i.e.,

uAP > max{

uPP , uP}

.

Note that Assumption 5 does not automatically imply that the agent is also hired in this

section. As will be shown below, if the maximum enforceable value of the bonus is too low,

performing the task herself (or abstaining) will be the principal’s optimal choice.

Furthermore, two aspects are worth mentioning. First of all, stationarity implies that if

hiring the agent is optimal in one period, this will also be optimal in all periods. Furthermore,

even if the agent is hired in equilibrium, the alternative of performing the task herself is still

important as an off-equilibrium outside option for the principal.

Concerning payoffs, stationarity implies that all periods are identical. Hence, we can omit

time subscripts and - in case the agent is hired - have discounted payoff streams

UAP =

−w + eA(H − b) + (1− eA)LA

1− δ

and

UA =w + eAb−

(

FA + kAe2A

2

)

1− δ.

If the agent is not hired, he receives a payoff of zero, whereas the principals has an outside

utility payoff stream UP = max

{

LP+(H−LP )2

2kP−FP

1−δ, uP

1−δ

}

, where the first component is the

utility level when the principal is active and the second when the principal abstains from the

task. We further assume that UP > LA − FA. Hence, it is not optimal to hire the agent

without giving incentives, i.e., for eA = 0.

Now, assume that the agent is hired and supposed to exert an effort level e∗A. A number

of constraints have to be satisfied for e∗A being part of an equilibrium. As before, the agent’s

incentive compatibility (IC) constraint must hold,

e∗A = argmaxUA (IC)

Due to stationarity, this condition is basically identical to the static game analyzed above.9

Hence, equilibrium effort can be obtained using the first-order approach, and equals

e∗A =b

kA.

9If we allowed for non-stationary equilibria, the bonus would generally not to be constant over time, sincefuture rents could be used to provide current incentives.

18

Furthermore, the agent’s individual rationality (IR) constraint and the limited liability

(LL) constraint are

UA ≥ 0 (IR)

w ≥ 0. (LL)

In addition, it must be optimal for the principal to actually make the bonus payment b.

As the outcome is not verifiable, the principal will only pay out b if it is optimal to do so.

This is the case whenever the future value of cooperation is higher than the future value of

non-cooperation, i.e. UP . Therefore, the principal’s dynamic enforcement (DE) constraint

equals

−b+ δUAP ≥ δU. (DE)

Note that whenever a strictly positive bonus and hence effort level can be enforced, then

UAP ≥ U , and hiring the agent is optimal. In this case, the objective is to maximize UA

P ,

subject to the constraints derived above.

In Appendix B, we fully characterize possible outcomes and show that if the principal’s

(DE) constraint does not bind, the results are identical to the static case derived above. Of

particular interest, though, is

Proposition 6: There exist values δ̂ and δ, with 0 < δ̂ < δ < 1, such that

• The agent is not hired if δ < δ̂

• The agent is hired, however equilibrium effort e∗Ais lower than in the static case if δ̂ ≤

δ < δ

• The agent is hired, and equilibrium effort e∗A is at the same level as in the static case if

δ ≥ δ

These results are driven by two aspects. First of all, the maximum enforceable bonus - and

hence maximum implementable effort - is determined by the principal’s (DE) constraint, and

increases in δ. If δ is rather large, the maximum enforceable effort is larger or equal than

the effort level induced in the static case, which then is implemented by the principal. If δ

gets smaller, enforceable effort goes down. At some point, it is so low and the likelihood of a

failure so large that it becomes optimal for the principal to either perform the task herself or

completely abstain from it.

Proposition 6 indicates that the main novelty of this section is the case when δ is between δ̂

and δ. Then, the agent is hired, however the principal would like to enforce a higher effort level

19

but cannot commit to compensate the agent accordingly. Proposition 6 also implies that a

higher δ increases the chances that hiring the PMSCs is actually optimal. The discount factor

δ reflects time preferences, but also the frequency of potential tasks for which the principal

considers hiring the agent. Hence, we should observe that countries that are hardly active in

(international) military operations should be less likely to hire contractors than those who are

repeatedly involved in large-scale projects.

In the remainder of this section, the parameters δ and UP are of particular interest to us,

and we want to explore their effect on the maximum enforceable value of b. In addition, we

examine what the respective values might actually imply for countries that consider hiring a

PMSC. All of the following results are proven in Appendix B.

In Proposition 7, we show that the higher the level of δ, the larger is the effort level that

can be enforced in an equilibrium maximizing the principal’s payoff stream.

Proposition 7: Assume δ̂ ≤ δ < δ. Then, equilibrium effort is strictly increasing in δ.

Whenever the (DE) constraint does not bind and hence not restrict equilibrium effort, a

higher δ has no impact on e∗A. However, if (DE) binds and the principal cannot commit to pay

a higher b to increase e∗A, a higher δ would directly increase effort and hence UAP . Therefore,

δ reflects the principal’s (expected) level of commitment in her relationship with the PMSC.

Furthermore, a binding (DE) constraint implies that not only total payoff streams increase

in δ, but also average, i.e., per-period payoffs. This is further captured by

Lemma 3: Assume δ̂ ≤ δ < δ. Then, per-period payoffs (1− δ)UAP are strictly increasing

in δ.

Furthermore, a higher outside option decreases the principal’s payoff in the case when

hiring the agent is optimal. This might seem counterintuitive, since generally a player should

always benefit from a better alternative option (for example, this is the case in bargaining sit-

uations). However, a higher outside option also reduces the ability of the principal to credibly

commit to reward the agent for successfully performing a task.

Proposition 8: Assume δ̂ ≤ δ < δ. Then, equilibrium effort is strictly decreasing in UP .

Furthermore, per-period payoffs (1− δ)UAP are strictly decreasing in UP .

Assuming that the value of not performing the task, uP , remains constant, the principal

might be able to affect UP if she is able to change parameters determing the value of being

active herself. For example, the size of the defense budget could generally affect operating

costs for a given mission or task. kP and FP might be lower if forces are better trained, or

20

could reflect opportunity costs if forces are not multifunctionally deployable. Hence, lower

investments into a country’s military might on the one hand have a direct impact on the use

of PMSCs - if the defense budget is reduced and the amount of activities remains constant,

it will naturally be optimal to let more of these activitivies be performed by PMSCs - and

might on the other hand have an indirect impact on the agent’s effort level: A lower outside

option increases the principal’s commitment, and hiring the agent becomes relatively better

compared to performing a given task herself. Hence, a reduction of the defense budget could

counteract a reduction of δ that is implied by a lower frequency of international activities.

In this section we endogenized the maximum enforceable value of b and showed under

which circumstances the principal can credibly commit to reward the agent. The most fun-

damental aspect here is the ability of the principal to implicitly forward an actual rent to

the agent after a task has been performed, i.e. for which a service in return is not directly

observable. Indeed, there is evidence that PMSCs receive rents (see Dickinson, 2007), how-

ever this practise is generally regarded as a problem - especially in terms of transparency and

corruption - that has to be tackled. Hence, competitive bidding processes are demanded as

a tool to fight corruption and enhance transparency. However, our results show that making

it impossible or generally harder to (at first sight unnecessarily) forward rents to PMSCs can

trigger unintended consequences: The principal’s inability to forward rents may reduce the

performance of PMSCs, and countries might either abstain or carry out task themselves where

hiring a PMSC would otherwise be optimal.

7 Impact on a Host State

In this section, we analyze one particular scenario, namely the setting in which an international

alliance untertakes a military intervention in another country (the host state), and individual

states hire PMSCs for specific military or security tasks to be carried ou in the host state.

When analyzing the impact of the use of PMSCs on the host state, it is less straightforward

to define whose preferences are relevant - whether it is the government or just some weighted

average of its inhabitants - especially if the purpose of the intervention is to replace the host

state’s government. Therefore, we confine on some general points on how the choice of the

principal affects the host state. Assume that if the mission does not take place, the host state’s

payoff is uH . If either the principal herself or the agent performs the task, a success triggers a

payoff HH , while a failure is associated with LH . Furthermore, a mission is always associated

with (expected) costs KH ≥ 0 for the host state, for example caused by the destruction of

infrastructure, loss of human lives, or disruption and polarization of the society. We do not

impose any assumptions on the size of HH and LH and KH . However, it seems sensible to

assume LH ≤ LP , i.e., the consequences of a failure of the task are more detrimental to the

host country than to any other player. HH could be larger or smaller than H. On the one

21

hand, a success of the task can have additional benefits to the host state that the principal

does not enjoy. On the other hand, the principal might enjoy reputational benefits that have

no impact on welfare in the host state. Generally, it makes most sense to assume that given

a task is being performed, the host state wants the job to be done as well as possible and

thus always prefers higher effort levels. As already pointed out, though, it might very well

be that the principal chooses the option with less effort (see Proposition 3). Generally, it is

possible that the principal’s and the host state’s preferences are sufficiently aligned. However,

the following cases can occur as well.

First of all, the principal might carry out a task even though the host state would have

preferred her to abstain. To have this outcome, uH and/or KH just have to be set sufficiently

high and uP sufficiently low. Concerning the latter, just consider domestic conditions making

an expansion of a mission very tempting for the principal. Furthermore, we might have

HP > HH . In this case, a potential victory would give the principal way more benefits than

the host state and thus make it optimal to carry out the task. The military interventions in

Afghanistan (2001) and Iraq (2003), for instance, illustrate this case.

Another potentially suboptimal outcome for the host state refers to the already mentioned

possibility that it might prefer the principal to carry out the task herself (especially if this was

associated with higher effort), but the latter would rather hire the agent. This would more

likely to happen for a larger difference between LA and LP (see Proposition 3). This outcome

is particularly critical when the PMSC exercises low effort in fulfilling the task. Host states

are normally war-ridden countries with very limited monitoring and oversight capacities. In

case of misconduct of PMSCs, for example, they most likely will not be able to prosecute them

appropriately as has for instance happened in Iraq, where employees of the PMSC Blackwater

International killed many Iraqi citizens in 2007. As Ross (2007, p. 95) puts it: ”[...] the Iraqi

government attempted to prosecute those involved. It was unable to do so because of Coalition

Provisional Authority (CPA) Order 17, which granted PMSCs and their personnel immunity

from Iraqi prosecution. Order 17 was repealed in one of the first acts of the Iraqi Parliament

in 2009, and the Ministry of Interior used its expanded authority to refuse Blackwater an

operating license. Despite decisive action by the Iraqi authorities, the company (now called

Xe Services) continues to operate in Iraq and is still the main provider of persnoal security

services for the U.S. State Department.”

8 Conclusion

We started our analysis from the basic questions (1) why states, while being aware of the

complicated agency dilemma inherent when hiring PMSCs, still rely on the services of these

companies and (2) how to set the right incentives for these companies to act according to the

best advantage of their principals. We developed a formal principal-agent moral hazard model

22

- with bounds on how well performance can be rewarded and bad performance be punished

- to explain some of the observed patterns in the relationship between PMSCs and states

potentially hiring them. The formal model yields three main results which advert to crucial

policy implications:

First, we showed that even if the agent is expected to do a worse job than the principal,

delegation can be optimal. Hence, an outcome that is not in the interest of the host state,

namely that the party expected to doing a worse job is selected for a given task, might occur.

The second major finding is that states which are not very active in international missions

should be less likely to hire PMSCs because of their inability to give PMSCs appropiate

incentives for exercising high effort. Even though in our analysis we considered the particular

relationship between a so-called strong state that hires a PMSC for services in a host state,

this result can also be applied to weak states that hire PMSCs in order to fill the gap left by

the inefficiency of their own security forces. Weak states often face the problem of not being

able to pay for these services. Then, the endowment with natural ressources might serve as a

subsitute to incentivize PMSCs - because they might expect to participate in the extraction

of natural ressources once the conflict is resolved. Early operations of PMSCs in ressource-

rich African countries seem to empirically support such a prediction.10 This result, however,

unfolds crucial implications regarding the commodification of security and the distribution of

security as a function of financial conditions, especially in weak states (see Krahmann 2008

and Leander 2005).

Thirdly, our analysis revealed that it is not only the PMSC’s reputation that is of practical

relevance, but more importantly the state’s credibility to keep the promise of a bonus (i.e.,

rehire the PMSC in future task and then grant it a rent) after a good outcome. Our model

suggests that this implicit promise is necessary in order to succesfully incentivize the agent to

exercise high effort. From a transparency-oriented point of view, this implicit promise may be

regarded as a form of corruption. This is reflected in the repeated requests for the enforcement

of competitive bidding processes when contracting PMSCs. Our results, however, indicate that

a high degree of transparency in the contracting process may have a negative impact on the

performance of PMSCs.

The results of this analysis contribute to the theoretical understanding of the implications

connected with the use of PMSCs by states and thus can serve as a base for further studies.

Extending the setup along different dimensions, for example, should provide more insights. The

process of how a specific agent is chosen could be analyzed, or several tasks might be regarded,

either being substitutes or complements with respect to benefits and costs. The latter aspect

seems especially worth pursuing, since it could help to capture the impact of a change in

the stability of the host state. If instability increases, it will often be optimal to extend a

mission, increasing the number of tasks to carry out and thus the possibility for PMSCs to10See Musah (2000) for a detailed description of the involvement of PMSCs in African conflicts.

23

be hired. The latter should - at least initially - benefit from a less stable environment, which

might even create perverse incentives on their side to engage in destabilizing activities (as

long as this engagement is not too obvious). However, at some point more instability will

also harm PMSCs. The reason is that more instability should increase the costs of effort (for

both parties) via two channels. On the one hand, costs are directly increased by a higher

demand for necessary resources. On the other hand, costs are indirectly affected because more

instability will decrease the success probability for a given effort level. To maintain a certain

success probability, more effort and thus more costly resources are necessary. Especially the

last point can consequently lead to a situation where totally abstaining from some task or

even an intervention as a whole will become optimal.

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Appendix A - Omitted Proofs for the Static Case

Proposition 2: Assume the agent is hired. Then, equilibrium effort depends on FA which

determines whether the agent has to get a rent. More precisly, there exist values FA and FA,

with FA < FA, such that

• Effort is at its efficient level, e∗A = eFBA = (H−LA)

kA, if FA ≥ FA. However, in this case

it can only be optimal to hire the agent if doing nothing is worth than a failure, i.e., if

uP < LA

27

• Effort is at half its efficient level, e∗A = (H−LA)2kA

, if FA < FA

• Effort lies between eFBA and

eFB

A

2 if FA ≤ FA < FA

Note that Proposition 2 is equivalent to

Proposition 2’: Assume the agent is hired. Then, equilibrium effort depends on FA which

determines whether the agent has to get a rent. More precisly,

• If FA ≥ (H−LA)2

2kA, effort is at its efficient level, e∗A = eFB

A = (H−LA)kA

. A necessary

condition for hiring the agent being optimal is uAP = e∗A (H − b) + (1 − e∗A)LA − w =

LA −(

FA − (H−LA)2

2kA

)

≥ uP , which can only be satisfied when LA > uP .

• If (H−LA)2

8kA< FA <

(H−LA)2

2kA, effort is inefficiently low and characterized by kA

(e∗A)2

2 −

FA = 0, where we further have(H−LA)

2kA< e∗A <

(H−LA)kA

. A necessary condition for hiring

the agent being optimal is LA +√

2FA

kA(H − LA)− 2FA ≥ uP , where

√

2FA

kA(H − LA)−

2FA > 0 and decreasing with FA.

• If FA ≤ (H−LA)2

8kA, effort is half the efficient level, i.e., e∗A = (H−LA)

2kA. A necessary condi-

tion for hiring the agent being optimal is(H−LA)2

4kA+ LA ≥ uP .

Proof : Given (IC), it is not necessary to impose the constraint b ≥ 0, as long as the optimal

effort choice is strictly positive (which will always be the case). Furthermore, we can use (IC)

to plug in b = e∗AkA into the principal’s problem, who is thus effectively able to choose effort.

Then, the Lagrange function equals

maxeA,w

L = eAH − e2AkA + (1− eA)LA − w + λIR

[

kAe2A

2 − FA + w]

+ λLLw.

First order conditions are

∂L

∂eA= (H − LA)− 2eAkA + λIRkAeA − λBkA = 0 (4)

∂L

∂w= −1 + λIR + λLL = 0 (5)

Complementary slackness conditions are

λIR

[

kAe2A

2 − FA + w]

= 0

λLLw = 0

λIR, λLL ≥ 0

Condition (5) implies that at least one of (IR) or (LL) has to bind. Analyzing all three

possible cases gives the results stated in the proposition.

(A) (IR) binds, λLL = 0.

28

Then, we can use λIR = 1 from (5) and plug it into (4), which becomes (H − LA) −

eAkA − λBkA = 0. Then, it will be optimal for the principal to implement first-best effort.

Thus, we have eFB if λB = 0. Furthermore, hiring the agent will not be dominated by staying

out of the targent country as long as uAP = e∗A(H − b) + (1 − e∗A)LA − w ≥ uP . We already

know that e∗A = H−LA

kAand b = e∗AkA. To obtain w, we use the fact that (IR) binds and thus

uA = e∗Ab + w − kA(e∗

A)2

2 − FA = 0 ⇒ w = FA − (H−LA)2

2kA. Plugging these values into the

entry condition gives LA −(

FA − (H−LA)2

2kA

)

≥ uP . Finally, this case is only feasible as long

as w = FA − (H−LA)2

2kA≥ 0.

(B) (LL) binds, λIR = 0, i.e., the agent gets a rent. Equation (4) now gives

e∗A =(H − LA)

2kA

Now, equilibrium effort is only half its first-best level. Thus, the need to give a rent to the

agent substantially reduces the implemented effort. The necessary condition to make entry

optimal (note that w = 0) becomes uAP = e∗A(H − b) + (1 − e∗A)LA = (H−LA)2

4kA+ LA ≥ uP .

Finally, this case is only feasible as long as uA = kAe2A

2 − FA = (H−LA)2

8kA− FA ≥ 0.

(C) (IR) and (LL) bind. From (A) and (B) it follows that the present case is relevant for(H−LA)2

8kA< FA <

(H−LA)2

2kA. Here, effort is thus characterized by binding (IR) and (LL) con-

straints, i.e., kAe2A

2 −FA = 0. Plugging in the boundaries of FA gives (H−LA)2kA

< e∗A <(H−LA)

kA.

Plugging this value into uAP further gives us the necessary condition for an entry being opti-

mal. There,√

2FA

kA(H − LA) − 2FA has to be non-negative because otherwise, the principal

could just enforce the same effort as in case (A), furthermore paying w = 0 and receiving

LA in expectation. More precisely,∂

√

2FA

kA(H−LA)−2FA

∂FA=

√

(H−LA)2

2kAFA− 2 ≤ 2 − 2 = 0. Thus,

√

2FA

kA(H − LA)−2FA ≥

√

2(H−LA)2

2kAkA

(H − LA)−2 (H−LA)2

2kA= (H−LA)2

kA− (H−LA)2

kA= 0. Q.E.D.

Lemma 2: Performing the task herself rather than hiring the agent becomes relatively bet-

ter for the principal for higher levels of LP , FA and kA, and for lower levels of LA, FB and

kB. The impact of a higher H is ambigous and depends on the size of kA, kP , LA and LP .

Proof to Lemma 2 : Immediately follows from differentiating uPP − uAP = LP − LA +(H−LP )2

2kP− (H−LA)2

2kA+ FA − FP (in the case of FA ≥ (H−LA)2

2kA), uPP − uAP = LP − LA +

(H−LP )2

2kP−√

2FA

kA(H − LA) − FP + 2FA (for (H−LA)2

8kA< FA <

(H−LA)2

2kA), or uPP − uAP =

LP − LA + (H−LP )2

2kP− (H−LA)2

4kA− FP (for FA <

(H−LA)2

8kA), taking into account that LA ≥ LP ,

kA ≤ kP and (H − LA) < kA. Q.E.D.

29

Proposition 3: A larger difference between LA and LP reduces uPP − uAP .

Proof to Proposition 3 : Define ∆L ≡ LA − LP ≥ 0 and plug it into uPP − uAP , further

keeping LP constant. Then,

• For FA ≥ (H−LA)2

2kA,∂(UP

P−UA

P )∂∆L

= −2+ (H−∆L−LP )kA

, which is negative due to Assumption

3 ((H − LA) < kA)

• For (H−LA)2

8kA< FA <

(H−LA)2

2kA,

∂(UP

P−UA

P )∂∆L

= −1 +√

2FA

kA. Since FA <

(H−LA)2

2kAand

(H − LA) < kA, −1 +√

2FA

kA≤ −1 + (H−LA)

kA< 0

• For FA <(H−LA)2

8kA,∂(UP

P−UA

P )∂∆L

= −1 + (H−(∆L+LP ))2kA

< 0

Q.E.D.

Appendix B - Endogenous b

Formal description

Time is discrete, future periods are discounted with the factor δ < 1. At the beginning of each

period t = 1, 2, ..., the principal either makes an offer to the agent (described by dPt = 1) or not

(dPt = 0). This offer consists of a verifiable component wt ≥ 0 and the promise to pay a bonus

bt ≥ 0 whenever yt = H. If dPt = 1, the agent decides whether to accept the offer or not, i.e.

chooses dAt ∈ {0, 1}. If the agent is actually hired in period t, i.e., if dt ≡ dPt dAt = 1, the fixed

component wt is forwarded to the agent, who subsequently chooses effort et ∈ [0, 1]. Then,

output Yt ∈ {H,LA} is realized, and the principal has the choice to pay the discretionary

bonus bt ≥ 0. Discounted payoff streams - given the agent is hired - are

UAP,t =

∞∑

τ=t

δt−τ[

dτ (−wτ + eA,τ (H − bτ ) + (1− eA,τ )LA) + (1− dτ )(1− δ)UP

]

UA,t =

∞∑

τ=t

δt−τdτ

(

wτ + eA,τ bτ −

(

FA + kAe2A,τ

2

))

,

where (1 − δ)UP = max{

LP + (H−LP )2

2kP− FP , uP

}

describes the principal’s optimal choice -

either perform the task herself or abstaining from it - in case the agent is not hired. There,

note that variable and fixed costs are constant over time and accrue in every period where the

agent is hired.

After reneging, i.e., the principal’s failure to make a promised payment b after a success

was observed, we assume that the principal is punished as harshly as possible. This implies

30

that the agent is not willing to exert positive effort in the future anymore and hence constitutes

a reversion to the static Nash equilibrium where the principal receives UP (see Abreu, Pearce,

Stacchetti (1990) for why this maximum punishment - which never occurs in equilibrium - is

optimal in a game like the one presented here).

The solution concept used is Public Perfect Equilibrium (see Fudenberg, Levine, and

Maskin, 1994). This describes a Nash equilibrium for each date t and history, together with

the assumption that players only use public strategies. The latter implies that any player’s

strategies only depend on publicly observable information. In particular, the agent’s strategies

are independent of his past effort choice. We are interested in the equilibrium that maximizes

the principal’s payoff, however impose a restriction to stationary contracts.

This gives constraints

w + kAe2A

2 − FA

1− δ≥ 0 (IR)

−eAkA+ δ

eAH + (1− eA)LA − w − e2AkA − max{

LP + (H−LP )2

2kP− FP , uP

}

1− δ

≥ 0, (DE)

where we already used b = eAkA from the agent’s (IC) constraint.

Then, we have the Lagrange function

L =eAH+(1−eA)LA−e2

AkA−w

(1−δ) +λIR

[

w−FA+kAe2A

2(1−δ)

]

+λDE

δeAH+(1−eA)LA−e2

AkA−w−max

{

LP+(H−LP )2

2kP−FP ,uP

}

(1−δ) −

λLLwL

and necessary conditions∂L∂w

= − 1(1−δ) + λIR

1(1−δ) − λDE

δ(1−δ) + λLL = 0

∂L∂eA

= H−LA−2eAkA(1−δ) + λIR

kAeA(1−δ) − λDEkA

[

2eAδ

(1−δ) + 1]

= 0

λIR

[

w−FA+kAe2A

2(1−δ)

]

= 0

λDE

[

δeAH+(1−eA)LA−e2

AkA−wL

(1−δ) − δUP − eAkA

]

= 0

λLLw = 0

λIR, λDE , λLL ≥ 0

These considerations already allows us to prove

Proposition 6: There exist values δ̂ and δ, with 0 < δ̂ < δ < 1, such that

31

• The agent is not hired if δ < δ̂

• The agent is hired, however equilibrium effort e∗Ais lower than in the static case if δ̂ ≤

δ < δ

• The agent is hired, and equilibrium effort e∗A is at the same level as in the static case if

δ ≥ δ

Proof: Note that if λDE = 0, this problem is identical to the static case. By Assumption 5, the

termeAH+(1−eA)LA−e2

AkA−w−max

{

LP+(H−LP )2

2kP−FP ,uP

}

(1−δ) is positive when effort eA is the same

as in the static case. This (together with eA ≤ 1 and hence bounded) implies that for δ → 1,

the constraint is satisfied for the static effort. Furthermore, note that the left hand side of

(DE) increases in δ. Combining both arguments proves the existence of δ. As a next step, note

that for δ = 0, this term is equal to −eAkA and hence negative for eA > 0, which - together

with the assumption that hiring the agent is not optimal for eA = 0 - establishes the exis-

tence of δ̂. Finally, note that the left hand side is increasing in δ, completing the proof. Q.E.D.

Generally, the following cases are possible:

δ ≥ δ, i.e., (DE) does not bind

If the principal’s (DE) constraint does not bind, the situation is basically identical to the

static case:

(A) (IR) binds, λLL = 0.

Then, we have λIR = 1 and hence eA = H−LA

kA, i.e. effort is at its efficient level. Since (IR)

binds, it can be used to obtain w, which equals w = FA − (H−LA)2

2kA. Hence, the conditions for

this case to hold are FA − (H−LA)2

2kA≥ 0 and - via (DE) -

δ1−δ

(

(H−LA)2

2kA+ LA − FA

)

− (H − LA) ≥ δUP . Note this is only feasible if UP < 0, since

the left hand side of this condition is negative.

(B) (LL) binds, λIR = 0, i.e., the agent gets a rent. Then, we have eA = H−LA

2kA. Conditions

for this case to hold are FA − (H−LA)2

8kA≤ 0 and δ

(1−δ)

[

(H−LA)2

4kA+ LA

]

− H−LA

2 ≥ δUP

(C) (IR) and (LL) bind. From (A) and (B) it follows that the present case is relevant for(H−LA)2

8kA< FA <

(H−LA)2

2kA. Effort is characterized by binding (IR) and (LL) constraints, i.e.,

eA =√

2FA

kA. Plugging in the boundaries of FA gives (H−LA)

2kA< eA <

(H−LA)kA

.

Furthermore, now (DE) is satisfied as long as δ

√

2FA

kAH+(1−

√

2FA

kA)LA−2FA

(1−δ) −δUP−√

2FA

kAkA ≥

0

32

(D) λLL = λIR = 0

This case is not feasible, since it would imply − 1(1−δ) = 0

δ̂ ≤ δ < δ, i.e., (DE) binds but the task is delegated to the agent

(A) (IR) binds, λLL = 0.

Then, w = FA − kAe2A

2 , and effort is characterized by δeAH+(1−eA)LA−FA−kA

e2A

2(1−δ) − δUP −

eAkA = 0, at least as long as this is solved by a strictly positive effort level. Note that effort

is inefficiently small in this case:

λIRA = 1 + δλDE

H−LA−eAkA(1−δ) − λDEkA

[

eAδ

(1−δ) + 1]

= 0

(B) (LL) binds, λIR = 0.

Then, w = 0, and effort is characterized by δeAH+(1−eA)LA−e2

AkA

(1−δ) − δUP − eAkA = 0, at

least as long as this is solved by a strictly positive effort level. Furthermore, eA < H−LA

2kA, since

H−LA−2eAkA(1−δ) − λDEkA

[

2eAδ

(1−δ) + 1]

= 0

(C) (IR) and (LL) bind.

Since w = 0, this case only reflects one point, namely where the conditions δ eAH+(1−eA)LA−e2AkA

(1−δ) −

δUP − eAkA = 0 and −FA + kAe2A

2 = 0 give the same effort level.

To see that effort is continuous around that point we the binding (DE) constraints in cases

(A) and (B), i.e., δeAH+(1−eA)LA−FA−kA

e2A

2(1−δ) −δUP−eAkA = δ

eAH+(1−eA)LA−e2AkA

(1−δ) −δUP−eAkA,

which is satisfied for −FA + kAe2A

2 = 0, namely where (IR) binds. Hence, eA < H−LA

2kAhere as

well.

(D) λLL = λIR = 0

This case is not feasible, since it would imply − 1(1−δ) − λDE

δ(1−δ) = 0.

This analysis further allows us to prove

Proposition 7: Assume δ̂ ≤ δ < δ. Then, equilibrium effort is strictly increasing in δ.

Proof : If the (DE) constraint binds, equilibrium effort is characterized by δeAH+(1−eA)LA−FA−kA

e2A

2(1−δ) −

δUP−eAkA = 0 (w > 0) or δ eAH+(1−eA)LA−e2AkA

(1−δ) −δUP−eAkA = 0 (w = 0). Thus, the implicit

function theorem gives deAdδ

=

−

1(1−δ)2

(

eAH+(1−eA)LA−FA−kAe2A

2

)

−UP

δH−LA−kAeA

(1−δ)−kA

if w > 0

−1

(1−δ)2(eAH+(1−eA)LA−e2

AkA)−UP

δH−LA−2eAkA

(1−δ)−kA

if w = 0

. To see that

both expression must be positive, first note that the denominators, the partial derivatives of

33

(DE) with respect to eA, must be negative. If any of them were positive, a higher effort level

would relax the constraint, contradicting that (DE) binds and eA is inefficiently small at the

same time (what we established above). Furthermore, nominators have to be positive. In the

first case a binding (DE) constraint implieseAH+(1−eA)LA−FA−kA

e2A

2(1−δ) −UP = eAkA

δ. Hence, we

have 1(1−δ)2

(

eAH + (1− eA)LA − FA − kAe2A

2

)

−UP ≥ 1(1−δ)

(

eAH + (1− eA)LA − FA − kAe2A

2

)

−

UP = eAkAδ

> 0. Equivalent considerations help to establish that the nominator of the second

expression - i.e. when (LL) binds - is positive as well. Q.E.D.

Furthermore, we can prove

Lemma 3: Assume δ̂ ≤ δ < δ. Then, per-period payoffs (1− δ)UAP are strictly increasing

in δ.

Proof : The principal’s per-period payoffs are (1−δ)UAP =

eAH + (1− eA)LA − kAe2A

2 − FA if w > 0

eAH + (1− eA)LA − e2AkA if w = 0,

withd((1−δ)UA

P )dδ

=

deAdδ

(H − LA − eAkA) if w > 0

deAdδ

(H − LA − 2eAkA) if w = 0. Above, we established that H −LA −

eAkA > 0 (w > 0) and H − LA − 2eAkA > 0 (w = 0), which together with Proposition 7

(deAdδ

> 0 if the (DE) constraint binds) proves the Lemma. Q.E.D.

Finally we prove

Proposition 8: Assume δ̂ ≤ δ < δ. Then, equilibrium effort is strictly decreasing in UP .

Furthermore, per-period payoffs (1− δ)UAP are strictly decreasing in UP .

Proof : Now, we have

deAdUP

=

δ

δH−LA−kAeA

(1−δ)−kA

if w > 0

δ

δH−LA−2eAkA

(1−δ)−kA

if w = 0> 0, since the denominators must be negative (see the

proof to Proposition ). Again, the principal’s per-period payoffs are (1−δ)UAP =

eAH + (1− eA)LA − kAe2A

2 − F

eAH + (1− eA)LA − e2AkA

withd((1−δ)UA

P )dUP

=

deAdUP

(H − LA − eAkA) if w > 0

deAdUP

(H − LA − 2eAkA) if w = 0, which is strictly negative if the (DE)

constraint binds. Q.E.D.

34